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Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 360, pp. 122 - 130
We study the mean-square stabilizability of Itô stochastic systems with delayed input. In contrast to most previous results, where only sufficient condition... 
Receding horizon control | Itô systems | Lyapunov type inequality | Delayed input | Stabilization | School construction
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 16
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 248, Issue 5, pp. 1230 - 1255
In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone... 
Demicontinuous | Burkholder inequality | Asymptotic stability | Mild solution | Itô-type inequality | Semi-monotone | MATHEMATICS | EXPONENTIAL STABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | Ito-type inequality | UNIQUENESS
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 10/2017, Volume 43, Issue 5, pp. 1287 - 1299
Journal Article
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, ISSN 1735-8515, 10/2017, Volume 43, Issue 5, pp. 1287 - 1299
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered. The coefficients are... 
MATHEMATICS | Levy noise | Stochastic evolution equation | Ito type inequality | stochastic convolution integral | monotone operator
Journal Article
Random Operators and Stochastic Equations, ISSN 0926-6364, 09/2015, Volume 23, Issue 3, pp. 151 - 159
In this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itô integrals. These inequalities generalize some inequalities which... 
Gronwall–Bellman inequality | Itô integral | 60H10 | 54C60 | Stochastic differential equation | Ito integral | Gronwall-Bellman inequality | Inequalities (Mathematics) | Stochastic differential equations | Analysis | Differential equations | Stochastic models | Operators | Integrals | Mathematical analysis | Uniqueness | Inequalities | Nonlinearity | Stochasticity
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 2012, Volume 15, Issue 2, pp. 423 - 436
Journal Article
REVSTAT-STATISTICAL JOURNAL, ISSN 1645-6726, 11/2007, Volume 5, Issue 3, pp. 249 - 267
Bounds on the large deviations probability of the maximum likelihood estimator and regular Bayes estimators, and Berry-Esseen type bound for the suitably... 
maximum likelihood estimator | Berry-Esseen type inequality | Bayes estimators | nonhomogeneous diffusion processes | STATISTICS & PROBABILITY | larger deviations probability | Ito stochastic differential equation | drift parameter
Journal Article
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 3, pp. 2121 - 2167
We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in... 
MARTINGALES | MATHEMATICS, APPLIED | Ito formula | exponential estimate | Burkholder-Davis-Gundy inequality | martingale type r Banach space | stochastic convolution | maximal inequality
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 2000, Volume 3, Issue 4, pp. 593 - 614
In this paper, we consider the exponentially asymptotic stability of the mild solutions of semilinear stochastic evolution equations of monotone type. An... 
Borel-Cantelli's lemma | Sample-path stability | Itô-type inequality | Stability in the p-th moment | Stochastic evolution equations | MATHEMATICS | EXPONENTIAL STABILITY | Ito-type inequality | stochastic evolution equations | PARTIAL-DIFFERENTIAL EQUATIONS | INEQUALITY | sample-path stability | stability in the p-th moment
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 04/2017, Volume 123, pp. 23 - 26
A concentration inequality for a specific type of the Itô integrals indexed by matrices is obtained. This type of stochastic processes appears in the framework... 
Itô integral | Concentration inequality | Nonparametric function estimation | Ito integral | STATISTICS & PROBABILITY | Analysis | Gaussian processes | Equality
Journal Article
Stochastics and Stochastic Reports, ISSN 1045-1129, 03/1995, Volume 53, Issue 1-2, pp. 129 - 174
A semigroup approach is used to prove existence, uniqueness and boundedness of the solution of semilinear stochastic evolution equations with monotone... 
semigroup | semilinear | Ito type "energy" inequality | Stochastic evolution equations | monotone nonlinearities Burkholder type inequality | martingales
Journal Article
2016 35th Chinese Control Conference (CCC), ISSN 1934-1768, 07/2016, Volume 2016-, pp. 1820 - 1825
This paper is concerned with the problem of almost sure exponential stability and moment exponential stability for a class of stochastic parabolic complex... 
Neurons | Nonnegative semi-martingale convergence theorem | reaction diffusion | Stability analysis | Control theory | Delays | complex networks | strong Itô function | Biological neural networks | exponential stability | Convergence | Networks | Stability | Conferences | Neural networks | Inequalities | White noise | Diffusion
Conference Proceeding
Journal of Functional Analysis, ISSN 0022-1236, 10/2016, Volume 271, Issue 7, pp. 1764 - 1792
We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations... 
Multiplicative gradient-type Stratonovich noise | Killing vector field | Stochastic total variation flow | Stochastic variational inequality with singular diffusivity | TOMOGRAPHY | EXISTENCE | MATHEMATICS | ITOS FORMULA | Multiplicative gradient-type | Stratonovich noise | Differential equations | Probability | Analysis of PDEs | Mathematics
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 01/2003, Volume 21, Issue 1, pp. 161 - 181
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 1985, Volume 20, Issue 1, pp. 1 - 40
Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. Burkholder's inequalities prove to be an adequate tool to control the quadratic... 
Ito-type formulas | Burkholder's inequalities | N-parameter strong martingales | N-parameter strong martingales Ito-type formulas Burkholder's inequalities
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 10/2009, Volume 27, Issue 6, pp. 1201 - 1211
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2018, Volume 370, Issue 12, pp. 8521 - 8550
It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map... 
Ito-Lyons map | p-variation | SPACES | THEOREM | INEQUALITY | STOCHASTIC CALCULUS | SIGNALS | Besov space | MATHEMATICS | Riesz-type variation | RESPECT | INTEGRATION | Besov embedding | rough path | Controlled differential equation | DIFFERENTIAL-EQUATIONS DRIVEN | FRACTAL FUNCTIONS
Journal Article
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